The Washington Post first reported the discussions between the Republican Party leaders and Bryant about potentially filling Cochran’s seat were the seven-term senator to step down.

The governor’s spokesman confirmed to the Clarion-Ledger that Bryant and McConnell met. But he did not mention the political brew in Mississippi.

“Gov. Bryant was honored to meet with Sen. McConnell on Tuesday to discuss infrastructure and a range of issues important to Mississippi and America. Those conversations will remain private,” Bryant spokesman Clay Chandler said. “The governor, like many Mississippians, thinks Sen. Cochran’s service has made our state stronger.”

Cochran, 80, missed more than a month of legislative business last fall as he recovered from a “urology issue” in Mississippi. He was elected to a seventh term in 2014, beating his Democratic opponent by 22 points in the deep-red state. Lawmakers and analysts have speculated that he could retire before his term is up in 2021, though Cochran remains adamant he will continue on.

If Cochran does indeed step down, Bryant’s right-hand man, Lt. Gov. Tate Reeves, would be the leading candidate to replace him, per the Clarion-Ledger report.

Other names floated in Mississippi political circles are Rep. Gregg Harper and Secretary of State Delbert Hosemann.

Republican state senator Chris McDaniel, who challenged Bryant in 2014, would likely not be on the governor’s shortlist of potential appointments.